too many parameters in Burnham LD model and Pradel--confused

[prugh]

When I run the Burnham live and dead recover model with full time dependency for S, it gives me as many estimates as I have intervals--how is it calculating S for my last interval?
Also when I used a Pradel survival and lambda model with full time dependency in p, it gave me as many p estimates as time intervals. The CJS model gave the expected # of p and phi parameters (# intervals - 1). I am wondering why the Burnham and Pradel models are different--I did not see this addressed in the Markbook chapters or the original papers.

[JT Schloesser]

I am experiencing a similar problem and hope someone can help me out. I have 15 time periods and for Burnhams LD models, it gives me 15 parameter estimates for both S and r, but only 14 parameter estimates for F and p. I've checked all the settings and capture histories without finding any problems. I thought about just discounting the last parameter for S to give me 14 estimates, but my first estimate for S is 1, which is not compatible with my data. My best fit models all have either g*t, g+t or t interactions. I ran the model averaging procedure and still the same situation. Any ideas on which parameters I need to use or ways to fix this? First time MARK user by the way.

JTS

[cooch]

I am experiencing a similar problem and hope someone can help me out. I have 15 time periods and for Burnhams LD models, it gives me 15 parameter estimates for both S and r, but only 14 parameter estimates for F and p. I've checked all the settings and capture histories without finding any problems. I thought about just discounting the last parameter for S to give me 14 estimates, but my first estimate for S is 1, which is not compatible with my data. My best fit models all have either g*t, g+t or t interactions. I ran the model averaging procedure and still the same situation. Any ideas on which parameters I need to use or ways to fix this? First time MARK user by the way.

JTS

Simple - if you have (n) occasions, for a LD model you have (n) estimates of survival, and (n-1) estimates for fidelity. Obvious explanation - you can't estimate fidelity for the interval following marking, since it is an 'event' that is estimable conditional on surviving beyond at least one interval. Encounter during the first interval is conditional only on survival and recovery rate. Encounter in subsequent intervals is a function of S, F, p, and r.

All you need to do is look at the individual PIMs for any fully dependent LD model. You'll see there are n index values for S, n-1 for p, n-1 for F, and n for r.

Pretty simple.

[Bill Kendall]

Evan is exactly right about the relative number of parameters for S, F, etc. In addition, although there are more S's than F's, the last S is not estimable in a fully time specific model. Its presence is an artifact of modeling recoveries as (1-S)r [Seber 1970] instead of as f [Brownie et al. 1985].

[cooch]

Evan is exactly right about the relative number of parameters for S, F, etc. In addition, although there are more S's than F's, the last S is not estimable in a fully time specific model. Its presence is an artifact of modeling recoveries as (1-S)r [Seber 1970] instead of as f [Brownie et al. 1985].

Thanks, Bill - forgot that little detail. The Seber parameterization (S and r) is strictly analogous to the standard phi/p CMR models, where the terminal phi and p values are not separately estimable in a fully time-specific model.

[cooch]

Evan is exactly right about the relative number of parameters for S, F, etc. In addition, although there are more S's than F's, the last S is not estimable in a fully time specific model. Its presence is an artifact of modeling recoveries as (1-S)r [Seber 1970] instead of as f [Brownie et al. 1985].

Thanks, Bill - forgot that little detail. The Seber parameterization (S and r) is strictly analogous to the standard phi/p CMR models, where the terminal phi and p values are not separately estimable in a fully time-specific model.

I've added a couple of paragraphs to Chapter 11 to make this clearer.